This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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6
votes
3answers
570 views

An introduction to wavelets, and the wavelet transform

I am looking for a good introduction to the wavelet transform, particularly in the context of image processing. I am very comfortable with the Fourier transforms, and I've got a good background in ...
3
votes
1answer
286 views

References for the basic theory of surfaces of revolution, cylinders and cones

I'm looking for references to books were the following types of problems about finding the equation defining a surface of revolution, a cylinder or a cone are treated. These are problems that are ...
4
votes
1answer
164 views

Dirichlet series generating function, ordinary generating function

I am partly repeating my self here. The sequence $a_n$ generated by the Dirichlet series generating function: $\sum \limits_{n=1}^{\infty} \frac{a_n}{n^s}$ corresponding to $\zeta(s)^m$ seems to ...
4
votes
2answers
356 views

Reference Request: Texts on Fourier Analysis with emphasis on Number Theory

This may not exist but I would just like to ask in case.. I think Rudin is probably the best book but it doesn't have any (?) number theory in it. What is a good textbook (or comprehensive lecture ...
2
votes
1answer
293 views

Name of a book with the following contents?

Some time ago, I received Algebra notes from my advisor who is advising me on a project. I learned very much from these notes and wondered what the name of the book from which these notes were ...
3
votes
0answers
39 views

Large Deviation Bounds for Number of Forests (or Tutte polynomial) in G(n,p)

Does anyone know of results/references related to large deviation bounds on the number of forests (or the Tutte polynomial) in G(n,p) (Erdos-Renyi random graphs)?
4
votes
4answers
748 views

Is there a good online dictionary/encyclopedia for mathematics?

I'm an engineer/physicist by training, and typically, my publications are in journals where the readers do have an semi-advanced understanding of math, but not at a serious mathematician's level. So ...
5
votes
2answers
305 views

publishing an article which contains abstract math and programming on arxiv or journal

I have a soft question. I currently study abstract math which includes group theory. On the other hand, I have strong background in c++, data structures etc. So, most of the time I end up with an ...
1
vote
3answers
330 views

references for the spectral theorem

Recently, I am thinking about the question in spectral theory. And I finally found that I need help with the properties of unitary operator. Its a consequence of the spectral theorem for the normal ...
2
votes
0answers
119 views

Question on the transversality between sections

Let $M^n$ be a differentiable manifold and $\pi\colon E\to M$ is $n$-dimensional vector bundle over $M$. We have a zero section $s\colon M\to E$ of $\pi$. How can I make a section $s'$ which is ...
13
votes
1answer
429 views

Transcendental Galois Theory

Is there a good reference on transcendental Galois Theory? More precisely, if $K/k$ admits a separating transcendence basis (or maybe if it is a separably generated extension) it seems to me that ...
11
votes
1answer
566 views

Hermite's solution of the general quintic in terms of theta functions

Can someone point me at or produce a translation or modern exposition of Hermite's solution of the general quintic in terms of theta functions? (the "before" and "after" steps are on the mathworld ...
4
votes
1answer
185 views

Reference / Survey article on automorphisms of groups

can one suggest a survey article on automorphisms of $p$ groups, and automorphisms of abelian groups/ abelian $p$ groups?
1
vote
2answers
231 views

Good book on Galois connections?

What are some good introductory books on Galois connections? I have read Galois Theory from Emil Artin, Algebra from Saunder Mac Lane, and I'm starting Serge Lang.
5
votes
0answers
178 views

Dual modules and first cohomology

Let $G$ be a finite group, $K$ a characteristic-$p$ algebraically closed field (say $p$ divides $|G|$), and let $M$ be a finite-dimensional $KG$-module. What hypotheses are needed on $G$, $M$ to ...
7
votes
3answers
135 views

graphs on surfaces

I'm looking for references on embedding graphs in surfaces (motivation: I was doodling and wondered how many distinct embeddings of $K_{3,3}$ into the torus there are.)
6
votes
1answer
583 views

Supplementary exercises for Herstein's Noncommutative Rings

I've been studying from the book Noncommutative Rings by Herstein (not as a part of some official course), but unfortunately it doesn't contain any exercises apart from a few simple ones in the body. ...
5
votes
1answer
623 views

Classification of lens space

Let $L(p,q)$ be the lens space, that is $L(p,q)=S^3/\mathbb{Z}_p$. Here, $\mathbb{Z}_p$ acts on $S^3$ by $(z_1,z_2)\mapsto (\rho z_1,\rho^q z_2)$, $ \rho=e^{\frac{2\pi i}{p}}$. It is well known ...
34
votes
8answers
46k views

What is the best book to learn probability?

Question is quite straight... I'm not very good in this subject but need to understand at a good level.
6
votes
5answers
1k views

discrete math book suitable for younger person?

When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens. Does anyone know if there are good books, ...
4
votes
2answers
587 views

The Strong Whitney Embedding Theorem-Any Recommended Sources?

Just about all of the standard textbooks on manifold theory give proofs of weak versions of the Whitney Embedding theorem. But other then Whitney's original 1944 paper,are there any standard sources ...
3
votes
2answers
536 views

Book for probability to be useful in machine learning

How would you recommend Sheldon Ross' A First Course In Probability for the purpose mentioned in the title? (i.e. to be of significant use while studying machine learning) An advice book on Linear ...
33
votes
7answers
7k views

Good books on Math History

I'm trying to find good books on the history of mathematics, dating as far back as possible. There was a similar question here Good books on Philosophy of Mathematics, but mostly pertaining to ...
4
votes
1answer
431 views

Proof of Liouville's Theorem(Conformal mappings)

I'm looking for a proof of Liouville's Theorem for conformal mappings. I can't find any proofs online in English (I'd settle for a German proof, though I'd take forever to read it. I cannot speak or ...
57
votes
23answers
23k views

What is a good complex analysis textbook?

I'm out of college, and trying to learn complex analysis on my own. I took out Ahlfors' text from the library, but I'm finding it difficult. Any textbook recommendations? I'm probably at an ...
4
votes
3answers
182 views

Books and Papers that have treatment of properties like Idempotence and related operations

Please recommend resources to study Idempotence and other similar properties of processes and operations in depth. I want to know what other properties like Idempotence are there for an operation. I ...
0
votes
1answer
98 views

reference for harmonic measure for planar domain

Hi I want to study harmonic measure for planar domain and its extension to higher dimension,could you tell me some books/papers on this topic starting from elementary?
3
votes
2answers
371 views

How to solve recurrence relations with emphasis on algorithmic complexity

I am having trouble solving recurrence relations, probably because I am missing the basics. Is there any web reference/book I can read to help me cover the basics? I watched some lectures and read ...
24
votes
11answers
6k views

Good books on Philosophy of Mathematics

Where can I learn more about the implications, meta discussions, history and the foundations of mathematics? Is Russell's Introduction to Mathematical Philosophy a good start?
9
votes
2answers
540 views

Is there any way to read articles without subscription?

This is not mathematician question but I think it's related. How I can get access to some of "Software: Practice and Experience" articles without subscription? Any advice is welcome. Sorry if I'm ...
5
votes
2answers
224 views

Logical relations between relations

I'm interested in properties of relations. Things like completeness (connected, total), transitivity, euclideanness, symmetry and so on. I am interested in the logical connections between these ...
8
votes
1answer
619 views

Translations of Darboux's “Leçons Sur La Théorie Générale Des Surfaces”

This might be slightly stretching the boundary of acceptable questions, but I think this is the best group to ask. I'm interested in the classic 1887 texts "Leçons Sur La Théorie Générale Des ...
7
votes
2answers
3k views

What are “Super Numbers”?

I'm reading Hyperspace by Michio Kaku and in the chapter on SuperGravity "Super Numbers" are mentioned and are described as a number system where for any super number $a$, $a*a=-a*a$. I was wondering ...
3
votes
1answer
111 views

Modelling a rail / underground / subway transportation system

I'm interested in creating a mathematical model of an underground (tube) system. The overall aim is being able to efficiently calculate travel times between stations. Such a system has some ...
4
votes
2answers
425 views

Excellent review/introduction for a future grad student in need

I recently graduated with a computer engineering degree and am now going to study neuroscience/neuro-engineering at the graduate level. I need to beef up on my linear algebra, differential equations, ...
3
votes
1answer
763 views

Proof of the classical div-curl-lemma

let $1 = \frac{1}{p} + \frac{1}{q}$ as usual. Let $f \in L^p, g \in L^q$ be vector fields from $\mathbb R^n$ to itself. Assume $div f = 0$ and there exists a function $G$ s.t. $\nabla G = g$. Then $f ...
1
vote
1answer
174 views

Solutions to a system of ODE's

I have been studying a particular ergodic system and it has become apparent that solutions to differential equations of the form $M(x,y,z,t)\begin{pmatrix} \frac{dx}{dt} \\ \frac{dy}{dt} \\ ...
3
votes
3answers
2k views

Good book for self-learning sequence and series

I would be very happy if it covers sequence and series from very basics to advanced. Thanks.:)
4
votes
5answers
606 views

Recursion theory text, alternative to Soare

I want/need to learn some recursion theory, roughly equivalent to parts A and B of Soare's text. This covers "basic graduate material", up to Post's problem, oracle constructions, and the finite ...
13
votes
5answers
2k views

Intuitive meaning of Limit Supremum?

I am trying to understand the difference between the following two equations: $$\bar{P} = \limsup_{t \to \infty}\frac{1}{t} \sum_{\tau = 0}^{t-1}E\{P[\tau]\} < \infty$$ and $$\bar{P} = \lim_{t ...
11
votes
2answers
692 views

Supplemental number theory text to Montgomery and Vaughan

We already have a large list of the Best ever book on Number Theory, but I'm looking for a more targeted response for analytic number theory. Specifically, I'm taking a trip on which I may or may ...
6
votes
2answers
604 views

Wreath product and solvability

A paper I'm reading claims that the smallest class of monoids which contains $\mathbb{Z}$ and is closed under finite direct product and block product only contains solvable monoids. I think that a ...
6
votes
1answer
214 views

Introductory texts for weak $\omega$-categories

As I'm constantly running across higher categories these days, I'm wondering what is a good starting point to get into the theory? While I am aware of nLab and the n-Category Café, I am having a real ...
10
votes
1answer
321 views

Chebyshev center = center of mass?

I would like to know for which convex polyhedra $P$ in $\mathbb{R}^3$, is the center of the largest sphere enclosed in $P$ (a.k.a. the Chebyshev center, or the incenter) the same as the center of ...
17
votes
2answers
2k views

Good introductory books on homological algebra

Which books would you recommend, for self-studying homological algebra, to a beginning graduate (or advanced undergraduate) student who has background in ring theory, modules, basic commutative ...
5
votes
1answer
785 views

How many real quadratic number fields have the class number 1?

I know that in general the number of ideal classes are not 1, and that there are only 9 imaginary quadratic number fields which are principal ideal domains, i.e. $\mathbb(Q(\sqrt{-m}))$ where m is 1, ...
1
vote
3answers
309 views

Can you help me translate this programming algorithm into mathematical language? Has prior work been done on the “LFSR” problem already?

There is this programming/mathematical problem I have; it is the problem of generating a sequence of n unique random numbers, where the random number $n$ is element of of the set $S = \{0, 1, 2, ...
1
vote
2answers
249 views

Where can I find Heegner's proof?

Where can I read a corrected up to date version of Heegner's solution of the class 1 problem of Gauss?
9
votes
2answers
668 views

Joint moments of Brownian motion

My approach to this SE question uses the following joint moments of Brownian motion. For $n=1,2$ they are obvious and well-known, the others are not terribly hard to work out. Is there a reference ...
4
votes
0answers
291 views

“Reverse thinking” exam questions-reference request

I am interested in exam questions that are "backwards" from how they are usually asked. For example: Brian and Megan have the following question on their exam: Find the volume of the solid ...